Camera calibration and 3D reconstruction have been studied for many years but is still an active research topic that arises in the fields of object modeling, mobile robot navigation and localization, and environment building amongst others. In all these applications there is a need to obtain 3D information of an object or scene from a 2D camera image.
In general, the problem of camera calibration and 3D reconstruction can be approached in three different ways. When both the intrinsic and extrinsic parameters of a vision system are known, the 3D reconstruction can easily be obtained by traditional triangulation methods. When the parameters of the vision system are totally uncalibrated, the 3D structure can be reconstructed up to a projective transformation from two uncalibrated images.
More usual than either of these extreme positions is the situation where the vision system may be assumed to have some of its intrinsic and extrinsic parameters calibrated while others are unknown. This may be referred to as a semi-calibrated vision system. Usually the intrinsic parameters are assumed to be known while the external parameters need to be calibrated.
It has been noted that in semi-calibrated vision systems the relative pose problem can also be solved from the correspondences between images of a scene plane. However, the computation efficiency for the pose problem is of critical importance particularly in robotic applications where planar surfaces are encountered frequently in a number of robotic tasks such as the navigation of a mobile robot along a ground plane, and the navigation of a wall climbing robot for the cleaning, inspection and maintenance of buildings. Traditional calibration methods such as the eight-point algorithm and the five-point algorithm will fail or give poor performance in planar or near planar environments since they require a pair of images from the three-dimensional scene.
Methods using only planar information have been explored. Hay (J. C Hay, “Optical motion and space perception; an extension of Gibson's analysis,” Psychological Review, Vol. 73, No. 6, pp. 550-565, 1966) was the first to report the observation that two planar surfaces undergoing different motions could give rise to the same image motion. Tsai et al. (R. Tsai, T Huang, “Estimating three-dimensional motion parameters of a rigid planar patch,” IEEE Trans. Acoust. Speech and Signal Process, Vol. ASSP-29, pp .525-534, 1981) used the correspondence of at least four image points to determine the two interpretations of planar surfaces undergoing large motions. Tsai et al. (R. Tsai, T Huang, and W. Zhu, “Estimating three dimensional motion parameters of a rigid planar patch, II: singular value decomposition,” IEEE Trans. Acoust. Speech and Signal Process, Vol. ASSP-30, pp. 525-534, 1982) later approached the same problem by computing the singular value decomposition of a 3×3 matrix containing eight “pure parameters.” Longuet-Higgins (H. C. Longuet-Higgins, “The visual ambiguity of a moving plane,” Proceedings of the Royal Society of London Series B, Vol. 223, No. 1231, pp. 165-175, 1984 and HC. Longuet-Higgins, “The reconstruction of a plane surface from two perspective projections,” Proceedings of the Royal Society of London Series B, Vol. 227, No. 1249, pp. 399-410, 1986) showed that three dimensional interpretations could be obtained by diagonalizing the 3×3 matrix, where the relative pose of the system and the normal vector of the planar surface could be achieved simultaneously by a second-order polynomial. Zhang et al (Z. Zhang, and A. R. Hanson, “Scaled Euclidean 3D reconstruction based on externally uncalibrated cameras,” IEEE International Symposium on Computer Vision, Coral Gables, Fla., November 1995, pp. 37-42) proposed a method for this problem from a case by case analysis of different geometric situations where as many as six cases were considered. Recently, Chen et al (S. Y Chen, and Y F Li, “Self-recalibration of a color-encoded light system for automated three-dimensional measurements,” Measurement Science and Technology, Vol. 14, No. 1, pp. 33-40, January 2003) also proposed a method for recalibrating a structured light system by using planar information and using a fundamental matrix with a minimum number of six points. In general, the prior art either requires the solution of high order equations or needs to consider many possible cases.